In this article, we optimally solve an integrated production and material handling scheduling problem. Traditionally, scheduling problems consider machines as the only constraining resource. This is however no longer true as material handling equipment are becoming more and more valuable resources requiring important investments. Their operations should be optimized and above all synchronized with machine operations. In the problem, addressed in this paper, a job-shop context is considered. Machines and material handling equipment (AGVs) are considered constraining resources. The shortest path between two machines is used for a material handling operation or an empty travel. A mathematical programming model and a constraint programming model are presented for the problem and solved optimally on test problems from the literature and larger instances that we generated. A commercial software (ILOG OPLStudio) was used for modeling, testing and integrating both models in a decision support system. The performance of the two methods is comparable when using the data from the literature. However, for larger instances the performance of the constraint programming model was superior to the mathematical programming model.